scholarly journals Complex variable solution for mode-III quadratically varying PS model in piezoelectric media

2021 ◽  
Vol 1033 ◽  
pp. 012044
Author(s):  
Sandeep Singh ◽  
Kuldeep Sharma
Keyword(s):  
Complex Variable ◽  
Mode Iii ◽  
Piezoelectric Media

scholarly journals A Mode-III strip saturation model for two collinear semi-permeable cracks in a piezoelectric media

2016 ◽  
Vol 3 (4) ◽  
pp. 1507-1519 ◽  
Author(s):  
R.R.Bhargava ◽  
◽  
Kamlesh Jangid ◽  
Pavitra Tripathi
Keyword(s):  
Saturation Model ◽  
Mode Iii ◽  
Piezoelectric Media

Dynamic Expansion Problems on Symmetrical Mode III Interface Crack

2011 ◽  
Vol 211-212 ◽  
pp. 1012-1015
Author(s):  
Nian Chun Lü ◽  
Yun Hong Cheng ◽  
Yun Tao Wang
Keyword(s):  
Interface Crack ◽  
Analytical Solutions ◽  
Complex Variable ◽  
Hilbert Problem ◽  
Mode Iii ◽  
Symmetrical Mode ◽  
Arbitrary Complex ◽  
Self Similar ◽  
Superposition Theorem ◽  
Riemann Hilbert Problem

By means of the complex variable functions, dynamic expension problems on symmetrical mode Ⅲ interface crack were researched. The problems considered can be very facilely transformed into Riemann-Hilbert problem by the measures of self-similar functions, and the general expressions of analytical solutions for the edges of mode Ⅲ symmetrical interface crack subjected to motive variable loadings Px2/t3 and Pt4/x3 were obtained by means of self-similar functions, respectively. After those solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be readily attained.

A Complex Variable Solution Based Analysis of Electric Displacement Saturation for a Cracked Piezoelectric Material

2014 ◽  
Vol 81 (9) ◽  
Author(s):  
Christian Linder
Keyword(s):  
Electric Fields ◽  
Complex Variable ◽  
Electric Displacement ◽  
Strain Energy Release ◽  
Mode Iii ◽  
Failure Initiation ◽  
Energy Release Rates ◽  
High Electric Fields ◽  
Strain Energy Release Rates ◽  
Ionic Movement

This paper presents an analysis of the effect of electric displacement saturation for a failing piezoelectric ceramic material based on a complex variable solution of a Mode III and a Mode I crack. This particular electric nonlinearity is caused by a reduction of the ionic movement in the material in the presence of high electric fields. Total and strain energy release rates are computed for varying far field stresses, electric displacements, and electric fields and compared for cases without and with full electric displacement saturation to further advance the understanding of failure initiation in piezoelectric ceramics.

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